Question:
In a pipe closed at one end, air column is vibrating in its third overtone. The air column has
In a pipe closed at one end, air column is vibrating in its third overtone. The air column has
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In a closed pipe the third overtone is the 7th harmonic. Count nodes and antinodes in that pattern.
Updated On: Nov 12, 2026
- three nodes and three antinodes
- three nodes and four antinodes
- four nodes and three antinodes
- four nodes and four antinodes
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
A pipe closed at one end has a node at the closed end and an antinode at the open end. It supports only odd harmonics: 1st, 3rd, 5th, 7th.
Step 2: Identify the mode
Fundamental, then first overtone (3rd harmonic), second overtone (5th), third overtone (7th harmonic). So \(L=\dfrac{7\lambda}{4}\).
Step 3: Count
Nodes and antinodes alternate, a quarter wavelength apart. The 7th harmonic has \(4\) nodes (including the closed end) and \(4\) antinodes (including the open end).
Final Answer:
The air column has four nodes and four antinodes. \[ \boxed{\text{(D) }\text{four nodes and four antinodes}} \]
A pipe closed at one end has a node at the closed end and an antinode at the open end. It supports only odd harmonics: 1st, 3rd, 5th, 7th.
Step 2: Identify the mode
Fundamental, then first overtone (3rd harmonic), second overtone (5th), third overtone (7th harmonic). So \(L=\dfrac{7\lambda}{4}\).
Step 3: Count
Nodes and antinodes alternate, a quarter wavelength apart. The 7th harmonic has \(4\) nodes (including the closed end) and \(4\) antinodes (including the open end).
Final Answer:
The air column has four nodes and four antinodes. \[ \boxed{\text{(D) }\text{four nodes and four antinodes}} \]
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